Holy Places of the World

Bethlehem, Israel: birthplace of Jesus
Nazareth, Israel: where Jesus lived and began ministry
Jerusalem, Israel: where the early Church was started

Catholic

The Vatican: also known as "Vatican City" and "The Holy See" (an independent state within Rome, Italy) [map]

Eastern Orthodox

Constantinople, Turkey: seat of the Patriarchate of Constantinople [photo gallery]
Mt. Athos - Mt. Athos is a peninsula in eastern Greece (near Thesaloniki) that is extremely revered by Orthodox believers. It is inhabited exclusively by monastics. There are twenty large monasteries plus countless small sketes, brotherhoods and hermitages. It is a major pilgramage sight for Orthodox males.

Anglican

Canterbury, England: seat of the Archbishop of Canterbury

Latter-day Saints

Salt Lake City, Utah: World headquarters of Church of Jesus Christ of Latter-day Saints; site of Salt Lake Temple, Temple Square, Mormon Tabernacle, etc.
Palmyra, New York: site of First Vision; city where Book of Mormon was first printed [map]
Kirtland, Ohio: site of first Latter-day Saint city; 1st temple
Nauvoo, Illinois: site of second Latter-day Saint city; 2nd temple (1st full-service temple) [map]